Experiments and Inference About Cause Section 4.3 Experiments and Inference About Cause

Recall, when we studied bivariate data which had a linear pattern, the LSRL and correlation were meaningful.

Did a strong correlation mean that a change in the predictor variable caused a change in the predicted variable?

No, because correlation does not imply causation. What could be responsible for the change?

No, because correlation does not imply causation. What else could be responsible for the change? A lurking variable

What is meant by “cause and effect”?

What is meant by “cause and effect”? A change in the explanatory variable causes the change in the response variable

What is difference between an experiment and an observational study?

Experiment: treatments randomly assigned to subjects

Experiment: treatments randomly assigned to subjects Observational study: no treatments get assigned to subjects by the experimenter conditions of interest (treatments) are already built into subjects being studied

A well-designed experiment is just about the only way to establish cause and effect.

A well-designed experiment is just about the only way to establish cause and effect. Why use good observational study if good, randomized experiment is nearly always better to conclude actual cause and effect?

Suppose we want to study the effects of second-hand smoke of the development of babies. Can we perform an experiment?

Suppose we want to study the effects of second-hand smoke of the development of babies. Can we perform an experiment? Of course not as we can not randomly assign the treatments of being exposed to smoke or not being exposed to smoke to the individual babies.

A well-designed experiment is just about the only way to establish cause and effect. Why use good observational study if good, randomized experiment is nearly always better to conclude actual cause and effect? May not be possible to assign treatments randomly to subjects

Goal of every experiment: establish cause by comparing two or more conditions, called treatments, using an outcome variable, called the response.

Design for Good Experiment

Design for Good Experiment 1) specific question to be answered

Design for Good Experiment 1) specific question to be answered 2) sufficient experimental units to allow replication - - people, animals, families, classrooms, etc to which treatments are randomly assigned

Replication Replication: a) random assignment of the same treatment to different units or b)

Replication Replication: a) random assignment of the same treatment to different units or b) random assignment of different treatments to same units over period of time

Replication Amount of info gained from experiment depends on number of repetitions The more data you have, the more faith you can have in your conclusions.

Design for Good Experiment 1) specific question to be answered 2) sufficient experimental units to allow replication 3) two or more well-defined treatments

Design for Good Experiment 3) two or more well-defined treatments - - standard treatment (status quo): comparison group

Design for Good Experiment 3) two or more well-defined treatments - - standard treatment (status quo): comparison group - - new treatment: treatment group

Design for Good Experiment 3) two or more well-defined treatments - - standard treatment (status quo): comparison group - - new treatment: treatment group - - no treatment (placebo): control group

Design for Good Experiment 1) specific question to be answered 2) sufficient experimental units to allow replication 3) two or more well-defined treatments 4) method of assigning treatments at random to subjects (experimental units)

Randomizing, when possible, protects against confounding in much the same way as it protects against bias in sampling

Randomizing, when possible, protects against confounding in much the same way as it protects against bias in sampling If you do not randomize, it’s risky to generalize your findings

What is confounding?

What is confounding? Two possible influences on an observed outcome are confounded if they are mixed together in a way that makes it impossible to separate their effects on the responses

Turn to page 246. Read the three paragraphs about the thymus example.

CONFOUNDING

Design for Good Experiment 4) method of assigning treatments at random to subjects (experimental units) If you assign treatments to units at random, then there are only two possible causes for a difference in the responses to the treatments. What are these two possibilities?

Design for Good Experiment If you assign treatments to units at random, then there are only two possible causes for a difference in the responses to the treatments. What are these two possibilities? (1) Either the treatment actually made the difference or (2)

Design for Good Experiment If you assign treatments to units at random, then there are only two possible causes for a difference in the responses to the treatments. What are these two possibilities? (1) Either the treatment actually made the difference or (2) difference happened just by chance

If probability is small that chance alone could cause the difference in the responses, then ?

If probability is small that chance alone could cause the difference in the responses, then you can infer that the cause of the difference was the treatment

Design for Good Experiment 5) specific response variable with clear directions for measuring it

Design for Good Experiment 5) specific response variable with clear directions for measuring it 6) protocol for handling experimental units to ensure units are treated as alike as possible except for the treatment assigned - - reduces/eliminates lurking variable

What is a blind experiment?

Design for Good Experiment Patients should not know what treatment they are receiving: “blind experiment”

What is a double blind experiment?

Design for Good Experiment Patients should not know what treatment they are receiving: “blind experiment” Doctors who evaluate how much patients’ symptoms are relieved should not know which treatment each patient receives: “double blind experiment” Why is this important?

Design for Good Experiment Patients should not know what treatment they are receiving: “blind experiment” Doctors who evaluate how much patients’ symptoms are relieved should not know which treatment each patient receives: “double blind experiment” - - prevents skewing results based on doctor’s personal belief about effectiveness of treatment

Design for Good Experiment 7) plan for analyzing results - - need to do this before starting experiment in case any other part of the design needs to be modified

Factors and Levels Factor: explanatory variable, usually categorical, in a randomized experiment or observational study

Factors and Levels Factor: explanatory variable, usually categorical, in a randomized experiment or observational study Level: one of the values or categories making up a factor

Factors and Levels

Factors and Levels What are the highlighted items?

Factors and Levels Highlighted items are the treatments.

For next example, identify: a) factors b) levels c) treatments d) experimental units e) response variable

A botanist was interested in determining the effects of scheduled watering (three days a week or daily) and the use of fertilizer (no fertilizer, traditional, or organic) in hopes of increasing the heat rating of jalapeño peppers. The botanist conducted his own experiment, assigning each combination of watering schedule and type of fertilizer to three plots at each of four chosen locations that had similar soil and full sun. The average final heat rating for each plot was then recorded at the end of the growing season.

A botanist was interested in determining the effects of scheduled watering (three days a week or daily) and the use of fertilizer (no fertilizer, traditional, or organic) in hopes of increasing the heat rating of jalapeño peppers. The botanist conducted his own experiment, assigning each combination of watering schedule and type of fertilizer to three plots at each of four chosen locations that had similar soil and full sun. The average final heat rating for each plot was then recorded at the end of the growing season.

A botanist was interested in determining the effects of scheduled watering (three days a week or daily) and the use of fertilizer (no fertilizer, traditional, or organic) in hopes of increasing the heat rating of jalapeño peppers. The botanist conducted his own experiment, assigning each combination of watering schedule and type of fertilizer to three plots at each of four chosen locations that had similar soil and full sun. The average final heat rating for each plot was then recorded at the end of the growing season.

How many treatments are there? What are they?

A botanist was interested in determining the effects of scheduled watering (three days a week or daily) and the use of fertilizer (no fertilizer, traditional, or organic) in hopes of increasing the heat rating of jalapeño peppers. The botanist conducted his own experiment, assigning each combination of watering schedule and type of fertilizer to three plots at each of four chosen locations that had similar soil and full sun. The average final heat rating for each plot was then recorded at the end of the growing season.

Treatments

Experimental units are ?

A botanist was interested in determining the effects of scheduled watering (three days a week or daily) and the use of fertilizer (no fertilizer, traditional, or organic) in hopes of increasing the heat rating of jalapeño peppers. The botanist conducted his own experiment, assigning each combination of watering schedule and type of fertilizer to three plots at each of four chosen locations that had similar soil and full sun. The average final heat rating for each plot was then recorded at the end of the growing season.

Experimental units are the 72 plots (assigning each combination of watering schedule and type of fertilizer to three plots at each of four chosen locations) 6(3)(4) = 72

Response variable?

A botanist was interested in determining the effects of scheduled watering (three days a week or daily) and the use of fertilizer (no fertilizer, traditional, or organic) in hopes of increasing the heat rating of jalapeño peppers. The botanist conducted his own experiment, assigning each combination of watering schedule and type of fertilizer to three plots at each of four chosen locations that had similar soil and full sun. The average final heat rating for each plot was then recorded at the end of the growing season.

Questions?